The data set contains 1989 records. The overall descriptive statistics:

##     Married     Meet credit history guidelines
##  No     : 678   0  : 171                      
##  Unknown:   3   1  :1816                      
##  Yes    :1308   666:   2                      
##                                               
##                                               
##                                               
##  Other obligations as a percent of total income non-Hispanic Black
##  Min.   : 0.00                                  No :1792          
##  1st Qu.:28.00                                  Yes: 197          
##  Median :33.00                                                    
##  Mean   :32.39                                                    
##  3rd Qu.:37.00                                                    
##  Max.   :95.00                                                    
##  Hispanic        Male      Mortgage loan approved
##  No :1878   No     : 369   No : 244              
##  Yes: 111   Unknown:  15   Yes:1745              
##             Yes    :1605                         
##                                                  
##                                                  
##                                                  
##  Loan amount/purchase price                 Race     
##  Min.   :  2.105            Hispanic          : 111  
##  1st Qu.: 70.000            non-Hispanic Black: 197  
##  Median : 80.000            non-Hispanic White:1681  
##  Mean   : 77.064                                     
##  3rd Qu.: 89.894                                     
##  Max.   :257.143

Descriptive statistics by Race:

## $Hispanic
##     MARRIED   GDLIN        OBRAT            MALE    APPROVE 
##  No     :31   0  :16   Min.   :14.60   No     :22   No :26  
##  Unknown: 1   1  :95   1st Qu.:29.00   Unknown: 2   Yes:85  
##  Yes    :79   666: 0   Median :33.00   Yes    :87           
##                        Mean   :33.46                        
##                        3rd Qu.:38.45                        
##                        Max.   :62.00                        
##     LOANPRC                       RACE    
##  Min.   : 39.39   Hispanic          :111  
##  1st Qu.: 80.00   non-Hispanic Black:  0  
##  Median : 89.39   non-Hispanic White:  0  
##  Mean   : 85.17                           
##  3rd Qu.: 90.42                           
##  Max.   :162.63                           
## 
## $`non-Hispanic Black`
##     MARRIED    GDLIN         OBRAT            MALE     APPROVE  
##  No     : 76   0  : 53   Min.   : 5.60   No     : 51   No : 64  
##  Unknown:  0   1  :144   1st Qu.:31.00   Unknown:  2   Yes:133  
##  Yes    :121   666:  0   Median :35.00   Yes    :144            
##                          Mean   :34.94                          
##                          3rd Qu.:38.90                          
##                          Max.   :63.00                          
##     LOANPRC                       RACE    
##  Min.   : 28.99   Hispanic          :  0  
##  1st Qu.: 80.00   non-Hispanic Black:197  
##  Median : 87.02   non-Hispanic White:  0  
##  Mean   : 83.97                           
##  3rd Qu.: 90.24                           
##  Max.   :255.52                           
## 
## $`non-Hispanic White`
##     MARRIED     GDLIN          OBRAT            MALE      APPROVE   
##  No     : 571   0  : 102   Min.   : 0.00   No     : 296   No : 154  
##  Unknown:   2   1  :1577   1st Qu.:27.60   Unknown:  11   Yes:1527  
##  Yes    :1108   666:   2   Median :32.50   Yes    :1374             
##                            Mean   :32.02                            
##                            3rd Qu.:36.50                            
##                            Max.   :95.00                            
##     LOANPRC                        RACE     
##  Min.   :  2.105   Hispanic          :   0  
##  1st Qu.: 68.182   non-Hispanic Black:   0  
##  Median : 79.888   non-Hispanic White:1681  
##  Mean   : 75.719                            
##  3rd Qu.: 89.623                            
##  Max.   :257.143

Descriptive statistics by Marital Status:

## $No
##     MARRIED    GDLIN         OBRAT            MALE     APPROVE  
##  No     :678   0  : 64   Min.   : 4.00   No     :252   No :102  
##  Unknown:  0   1  :614   1st Qu.:28.00   Unknown:  7   Yes:576  
##  Yes    :  0   666:  0   Median :33.00   Yes    :419            
##                          Mean   :32.74                          
##                          3rd Qu.:37.00                          
##                          Max.   :83.00                          
##     LOANPRC                        RACE    
##  Min.   :  2.105   Hispanic          : 31  
##  1st Qu.: 72.426   non-Hispanic Black: 76  
##  Median : 80.000   non-Hispanic White:571  
##  Mean   : 77.967                           
##  3rd Qu.: 89.978                           
##  Max.   :162.626                           
## 
## $Unknown
##     MARRIED  GDLIN       OBRAT           MALE   APPROVE    LOANPRC      
##  No     :0   0  :0   Min.   :13.0   No     :1   No :0   Min.   : 86.96  
##  Unknown:3   1  :3   1st Qu.:23.3   Unknown:0   Yes:3   1st Qu.: 88.62  
##  Yes    :0   666:0   Median :33.6   Yes    :2           Median : 90.29  
##                      Mean   :27.2                       Mean   : 98.16  
##                      3rd Qu.:34.3                       3rd Qu.:103.76  
##                      Max.   :35.0                       Max.   :117.24  
##                  RACE  
##  Hispanic          :1  
##  non-Hispanic Black:0  
##  non-Hispanic White:2  
##                        
##                        
##                        
## 
## $Yes
##     MARRIED     GDLIN          OBRAT            MALE      APPROVE   
##  No     :   0   0  : 107   Min.   : 0.00   No     : 116   No : 142  
##  Unknown:   0   1  :1199   1st Qu.:28.00   Unknown:   8   Yes:1166  
##  Yes    :1308   666:   2   Median :33.00   Yes    :1184             
##                            Mean   :32.22                            
##                            3rd Qu.:37.00                            
##                            Max.   :95.00                            
##     LOANPRC                        RACE     
##  Min.   :  8.772   Hispanic          :  79  
##  1st Qu.: 68.857   non-Hispanic Black: 121  
##  Median : 80.000   non-Hispanic White:1108  
##  Mean   : 76.547                            
##  3rd Qu.: 89.866                            
##  Max.   :257.143

Descriptive statistics by Gender:

## $No
##     MARRIED    GDLIN         OBRAT            MALE     APPROVE  
##  No     :252   0  : 31   Min.   : 6.99   No     :369   No : 50  
##  Unknown:  1   1  :338   1st Qu.:28.00   Unknown:  0   Yes:319  
##  Yes    :116   666:  0   Median :33.00   Yes    :  0            
##                          Mean   :32.64                          
##                          3rd Qu.:37.00                          
##                          Max.   :83.00                          
##     LOANPRC                       RACE    
##  Min.   : 11.01   Hispanic          : 22  
##  1st Qu.: 70.83   non-Hispanic Black: 51  
##  Median : 80.00   non-Hispanic White:296  
##  Mean   : 77.66                           
##  3rd Qu.: 90.00                           
##  Max.   :255.52                           
## 
## $Unknown
##     MARRIED  GDLIN        OBRAT            MALE    APPROVE 
##  No     :7   0  : 0   Min.   :24.00   No     : 0   No : 0  
##  Unknown:0   1  :15   1st Qu.:29.95   Unknown:15   Yes:15  
##  Yes    :8   666: 0   Median :34.50   Yes    : 0           
##                       Mean   :33.33                        
##                       3rd Qu.:37.65                        
##                       Max.   :40.30                        
##     LOANPRC                      RACE   
##  Min.   :39.39   Hispanic          : 2  
##  1st Qu.:74.93   non-Hispanic Black: 2  
##  Median :75.42   non-Hispanic White:11  
##  Mean   :75.59                          
##  3rd Qu.:80.43                          
##  Max.   :92.90                          
## 
## $Yes
##     MARRIED     GDLIN          OBRAT            MALE      APPROVE   
##  No     : 419   0  : 140   Min.   : 0.00   No     :   0   No : 194  
##  Unknown:   2   1  :1463   1st Qu.:28.00   Unknown:   0   Yes:1411  
##  Yes    :1184   666:   2   Median :33.00   Yes    :1605             
##                            Mean   :32.32                            
##                            3rd Qu.:37.00                            
##                            Max.   :95.00                            
##     LOANPRC                        RACE     
##  Min.   :  2.105   Hispanic          :  87  
##  1st Qu.: 69.655   non-Hispanic Black: 144  
##  Median : 80.000   non-Hispanic White:1374  
##  Mean   : 76.942                            
##  3rd Qu.: 89.881                            
##  Max.   :257.143

There are 3 records are missing married (MARRIED) field.

ID MARRIED GDLIN OBRAT BLACK HISPAN MALE APPROVE LOANPRC RACE
356 Unknown 1 35.0 No Yes Yes Yes 86.95652 Hispanic
759 Unknown 1 33.6 No No Yes Yes 90.28571 non-Hispanic White
1392 Unknown 1 13.0 No No No Yes 117.24140 non-Hispanic White

There are 3 records are missing married (GDLIN) field.

ID MARRIED GDLIN OBRAT BLACK HISPAN MALE APPROVE LOANPRC RACE
881 Yes 666 35 No No Yes Yes 75.82939 non-Hispanic White
1229 Yes 666 26 No No Yes Yes 100.00000 non-Hispanic White

There are 15 records are missing gender (MALE) field.

ID MARRIED GDLIN OBRAT BLACK HISPAN MALE APPROVE LOANPRC RACE
1 No 1 34.5 No No Unknown Yes 75.42373 non-Hispanic White
127 No 1 31.6 No No Unknown Yes 80.80000 non-Hispanic White
286 Yes 1 37.3 No No Unknown Yes 80.05337 non-Hispanic White
452 Yes 1 40.1 Yes No Unknown Yes 75.00000 non-Hispanic Black
618 Yes 1 38.5 No No Unknown Yes 92.90323 non-Hispanic White
695 Yes 1 25.0 No No Unknown Yes 64.48276 non-Hispanic White
762 Yes 1 27.6 No No Unknown Yes 75.55556 non-Hispanic White
768 No 1 35.6 No No Unknown Yes 64.74397 non-Hispanic White
833 Yes 1 24.0 No Yes Unknown Yes 79.80769 Hispanic
979 No 1 31.7 No No Unknown Yes 74.86033 non-Hispanic White
1040 No 1 38.0 Yes No Unknown Yes 75.38462 non-Hispanic Black
1070 Yes 1 40.3 No Yes Unknown Yes 39.39394 Hispanic
1092 Yes 1 29.7 No No Unknown Yes 90.10239 non-Hispanic White
1613 No 1 30.2 No No Unknown Yes 90.00000 non-Hispanic White
1924 No 1 35.8 No No Unknown Yes 75.32051 non-Hispanic White
##                     APPROVE
## RACE                   No  Yes
##   Hispanic             26   85
##   non-Hispanic Black   64  133
##   non-Hispanic White  154 1527

##          APPROVE
## MARRIED     No  Yes
##   No       102  576
##   Unknown    0    3
##   Yes      142 1166

##          APPROVE
## MALE        No  Yes
##   No        50  319
##   Unknown    0   15
##   Yes      194 1411

## , , RACE = Hispanic
## 
##          APPROVE
## MARRIED     No  Yes
##   No         7   24
##   Unknown    0    1
##   Yes       19   60
## 
## , , RACE = non-Hispanic Black
## 
##          APPROVE
## MARRIED     No  Yes
##   No        27   49
##   Unknown    0    0
##   Yes       37   84
## 
## , , RACE = non-Hispanic White
## 
##          APPROVE
## MARRIED     No  Yes
##   No        68  503
##   Unknown    0    2
##   Yes       86 1022

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + 
##     LOANPRC, family = "binomial", data = data)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##     1.53721      3.70447     -0.03525     -0.80680     -0.84499  
##       MALE1      LOANPRC  
##     0.14139     -0.01643  
## 
## Degrees of Freedom: 1971 Total (i.e. Null);  1965 Residual
## Null Deviance:       1476 
## Residual Deviance: 966   AIC: 980
##                   2.5 %       97.5 %
## (Intercept)  0.39043496  2.703252996
## GDLIN1       3.29115094  4.137733306
## OBRAT       -0.05549706 -0.015038547
## BLACK1      -1.26962817 -0.326297080
## HISPAN1     -1.42913599 -0.215005260
## MALE1       -0.30298683  0.565437899
## LOANPRC     -0.02663168 -0.006658542
##                   2.5 %       97.5 %
## (Intercept)  0.38363811  2.690789543
## GDLIN1       3.28199418  4.126951904
## OBRAT       -0.05547873 -0.015022012
## BLACK1      -1.27779072 -0.335818281
## HISPAN1     -1.45043209 -0.239548275
## MALE1       -0.29193829  0.574720492
## LOANPRC     -0.02635892 -0.006504892
## (Intercept)      GDLIN1       OBRAT      BLACK1     HISPAN1       MALE1 
##   4.6516120  40.6286322   0.9653637   0.4462819   0.4295616   1.1518751 
##     LOANPRC 
##   0.9837024
##                     OR      2.5 %     97.5 %
## (Intercept)  4.6516120  1.4776234 14.9282142
## GDLIN1      40.6286322 26.8737761 62.6606279
## OBRAT        0.9653637  0.9460148  0.9850740
## BLACK1       0.4462819  0.2809361  0.7215908
## HISPAN1      0.4295616  0.2395158  0.8065372
## MALE1        1.1518751  0.7386088  1.7602184
## LOANPRC      0.9837024  0.9737198  0.9933636

## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC, 
##     family = "binomial", data = data)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##     1.66644      3.69659     -0.03524     -0.81891     -0.84836  
##     LOANPRC  
##    -0.01652  
## 
## Degrees of Freedom: 1971 Total (i.e. Null);  1966 Residual
## Null Deviance:       1476 
## Residual Deviance: 966.4     AIC: 978.4
## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + 
##     LOANPRC, family = binomial(link = "probit"), data = data)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##     0.64766      2.13928     -0.01705     -0.42091     -0.43124  
##       MALE1      LOANPRC  
##     0.06307     -0.00827  
## 
## Degrees of Freedom: 1971 Total (i.e. Null);  1965 Residual
## Null Deviance:       1476 
## Residual Deviance: 965.5     AIC: 979.5
##            Overall
## GDLIN1  17.7034125
## OBRAT    3.1949750
## BLACK1   3.3211862
## HISPAN1  2.6512623
## MALE1    0.5695835
## LOANPRC  3.2178042
## 
## Call:  glm(formula = APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC, 
##     family = binomial(link = "probit"), data = data)
## 
## Coefficients:
## (Intercept)       GDLIN1        OBRAT       BLACK1      HISPAN1  
##    0.706553     2.136046    -0.017060    -0.427179    -0.432845  
##     LOANPRC  
##   -0.008317  
## 
## Degrees of Freedom: 1971 Total (i.e. Null);  1966 Residual
## Null Deviance:       1476 
## Residual Deviance: 965.8     AIC: 977.8
##           Overall
## GDLIN1  17.702452
## OBRAT    3.197948
## BLACK1   3.383556
## HISPAN1  2.662084
## LOANPRC  3.236990
## Analysis of Deviance Table
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1      1965     965.48                     
## 2      1966     965.80 -1  -0.3199   0.5717
## Likelihood ratio test
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + LOANPRC
##   #Df  LogLik Df  Chisq Pr(>Chisq)
## 1   7 -482.74                     
## 2   6 -482.90 -1 0.3199     0.5717
## 
## Call:  glm(formula = APPROVE ~ GDLIN + BLACK + HISPAN + MALE + LOANPRC, 
##     family = binomial(link = "probit"), data = data)
## 
## Coefficients:
## (Intercept)       GDLIN1       BLACK1      HISPAN1        MALE1  
##    0.105974     2.184604    -0.441909    -0.441348     0.064210  
##     LOANPRC  
##   -0.009121  
## 
## Degrees of Freedom: 1971 Total (i.e. Null);  1966 Residual
## Null Deviance:       1476 
## Residual Deviance: 977.2     AIC: 989.2
##            Overall
## GDLIN1  18.2133105
## BLACK1   3.4982924
## HISPAN1  2.7352593
## MALE1    0.5837877
## LOANPRC  3.6344426
## Analysis of Deviance Table
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + MALE + LOANPRC
##   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
## 1      1965     965.48                          
## 2      1966     977.18 -1  -11.697 0.0006261 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Likelihood ratio test
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + MALE + LOANPRC
##   #Df  LogLik Df  Chisq Pr(>Chisq)    
## 1   7 -482.74                         
## 2   6 -488.59 -1 11.697  0.0006261 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:  glm(formula = APPROVE ~ GDLIN + BLACK + HISPAN + LOANPRC, family = binomial(link = "probit"), 
##     data = data)
## 
## Coefficients:
## (Intercept)       GDLIN1       BLACK1      HISPAN1      LOANPRC  
##    0.165274     2.181533    -0.448539    -0.443199    -0.009168  
## 
## Degrees of Freedom: 1971 Total (i.e. Null);  1967 Residual
## Null Deviance:       1476 
## Residual Deviance: 977.5     AIC: 987.5
##           Overall
## GDLIN1  18.213136
## BLACK1   3.565111
## HISPAN1  2.748035
## LOANPRC  3.654179
## Analysis of Deviance Table
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + LOANPRC
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)   
## 1      1965     965.48                        
## 2      1967     977.52 -2  -12.033 0.002438 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Likelihood ratio test
## 
## Model 1: APPROVE ~ GDLIN + OBRAT + BLACK + HISPAN + MALE + LOANPRC
## Model 2: APPROVE ~ GDLIN + BLACK + HISPAN + LOANPRC
##   #Df  LogLik Df  Chisq Pr(>Chisq)   
## 1   7 -482.74                        
## 2   5 -488.76 -2 12.033   0.002438 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1